We report the spectral index of diffuse radio emission between 50 and 100 MHz from data collected with two implementations of the Experiment to Detect the Global EoR Signature (EDGES) low-band system. EDGES employs a wide-beam zenith-pointing dipole antenna centred on a declination of −26.7°. We measure the sky brightness temperature as a function of frequency averaged over the EDGES beam from 244 nights of data acquired between 2016 September 14 and 2017 August 27. We derive the spectral index, β, as a function of local sidereal time (LST) using night-time data and a two-parameter fitting equation. We find −2.59 < β < −2.54 ± 0.011 between 0 and 12 h LST, ignoring ionospheric effects. When the Galactic Centre is in the sky, the spectral index flattens, reaching β = −2.46 ± 0.011 at 18.2 h. The measurements are stable throughout the observations with night-to-night reproducibility of σβ < 0.004 except for the LST range of 7 to 12 h. We compare our measurements with predictions from various global sky models and find that the closest match is with the spectral index derived from the Guzmán and Haslam sky maps, similar to the results found with the EDGES high-band instrument for 90–190 MHz. Three-parameter fitting was also evaluated with the result that the spectral index becomes more negative by ∼0.02 and has a maximum total uncertainty of 0.016. We also find that the third parameter, the spectral index curvature, γ, is constrained to −0.11 < γ < −0.04. Correcting for expected levels of night-time ionospheric absorption causes β to become more negative by 0.008–0.016 depending on LST.